My income is higher than the AMT exemption. But the amt calculated by Turbotax is smaller than the regular tax calculated by Turbotax. Is this is unusual?

look at form 6251 for AMT computation

It is not unusual since your AMT income may be less than your adjusted gross income (AGI), so you need to know more than what your AMT exemption and AGI is to draw conclusions regarding your AMT tax. You can view the form 6251 on your tax return to see how it is calculated.